Exploratory Plots for 2017-2018 Acoustic/Fish Data

Purpose To explore the Acoustic data gathered in 2017 and 2018 to expose important trends between sites, diurnal patterns, fish abundance, lunar phase, and coral reef acoustics.

Validations

Combined Model All variables are matched to the files that were used for Fish call counts (3:00, 9:00, 15:00, 21:00)

Confidence Intervals

Distributions

Red is the Mean Line

Blue is the Median Line

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Stats for Mid Frequency SPL

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   100.2   103.4   104.7   105.8   107.7   119.3

Variance of MF

## [1] 11.87399

Stats for High Frequency SPL

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   100.4   114.5   117.2   117.1   119.2   129.1

Variance of HF

## [1] 11.96909

ACI histogram

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Regressions

Running basic regressions linking the explanatory to the response at their lowest levels and combined to see how different sites/ hours change the regression - SPL

Linear Model outputs below each

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = Snap.HF17)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.8309 -1.9842  0.2062  1.8451 13.3944 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.053e+02  6.541e-01  160.99   <2e-16 ***
## Snaps       7.227e-03  4.475e-04   16.15   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.807 on 10163 degrees of freedom
## Multiple R-squared:  0.02502,    Adjusted R-squared:  0.02493 
## F-statistic: 260.8 on 1 and 10163 DF,  p-value: < 2.2e-16

2017 Snap data, snaps significant.

When you break it down by site, site 32 has the opposite relationship with high frequency and snaps.

High Frequency

2017 Snap/HF SPL Site Breakdown

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s17s5)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.0817 -2.1540  0.4371  1.9805  7.0937 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 87.830664   1.873329   46.88   <2e-16 ***
## Snaps        0.018381   0.001277   14.39   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.483 on 2101 degrees of freedom
## Multiple R-squared:  0.08971,    Adjusted R-squared:  0.08928 
## F-statistic: 207.1 on 1 and 2101 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s17s8)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.3374 -1.3945  0.1363  1.4230  9.4265 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 7.185e+01  1.270e+00   56.59   <2e-16 ***
## Snaps       3.314e-02  9.084e-04   36.48   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.117 on 1831 degrees of freedom
## Multiple R-squared:  0.4209, Adjusted R-squared:  0.4206 
## F-statistic:  1331 on 1 and 1831 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s17s35)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9213 -1.7565 -0.0424  1.6512 10.3407 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 71.282701   1.451690   49.10   <2e-16 ***
## Snaps        0.029598   0.000995   29.75   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.573 on 2205 degrees of freedom
## Multiple R-squared:  0.2864, Adjusted R-squared:  0.2861 
## F-statistic: 884.9 on 1 and 2205 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s17s40)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.1902 -1.2312  0.0344  1.2186  9.3897 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 7.644e+01  1.044e+00   73.19   <2e-16 ***
## Snaps       2.679e-02  7.062e-04   37.93   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.736 on 1862 degrees of freedom
## Multiple R-squared:  0.4359, Adjusted R-squared:  0.4356 
## F-statistic:  1439 on 1 and 1862 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s17s32)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -4.936 -1.084  0.114  1.063  7.102 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 137.43721    0.89844  152.97   <2e-16 ***
## Snaps        -0.01414    0.00060  -23.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.532 on 2156 degrees of freedom
## Multiple R-squared:  0.2047, Adjusted R-squared:  0.2044 
## F-statistic:   555 on 1 and 2156 DF,  p-value: < 2.2e-16

2018 Snap/HF SPL

Removing outliers

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = Snap.HF18)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.6746 -2.0071 -0.0087  2.3005 12.6859 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 81.468599   1.919126   42.45   <2e-16 ***
## Snaps        0.025921   0.001315   19.71   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.072 on 1453 degrees of freedom
## Multiple R-squared:  0.211,  Adjusted R-squared:  0.2105 
## F-statistic: 388.7 on 1 and 1453 DF,  p-value: < 2.2e-16

2018 Snap data with outliers removed. Snaps significant.

When split by sight, site 32 has a flat relationship.

2018 Snap/HF SPL Site Breakdown

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s18s5)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.9245 -1.5844  0.1253  1.6517  5.3652 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 60.225493   4.141984   14.54   <2e-16 ***
## Snaps        0.038216   0.002823   13.54   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.238 on 289 degrees of freedom
## Multiple R-squared:  0.388,  Adjusted R-squared:  0.3859 
## F-statistic: 183.2 on 1 and 289 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s18s8)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.7323 -1.3490 -0.0334  1.4302  4.1632 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 68.048894   2.745679   24.78   <2e-16 ***
## Snaps        0.035631   0.001889   18.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.849 on 289 degrees of freedom
## Multiple R-squared:  0.5519, Adjusted R-squared:  0.5504 
## F-statistic:   356 on 1 and 289 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s18s35)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9232 -1.1784 -0.1059  1.0416  7.5440 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 83.11812    1.96366   42.33   <2e-16 ***
## Snaps        0.02652    0.00133   19.94   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.739 on 289 degrees of freedom
## Multiple R-squared:  0.5791, Adjusted R-squared:  0.5776 
## F-statistic: 397.6 on 1 and 289 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s18s40)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.4914 -1.3764 -0.1106  1.2747  6.8204 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 68.686141   2.640335   26.01   <2e-16 ***
## Snaps        0.033362   0.001816   18.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.869 on 289 degrees of freedom
## Multiple R-squared:  0.5388, Adjusted R-squared:  0.5372 
## F-statistic: 337.7 on 1 and 289 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SPL_HF ~ Snaps, data = s18s32)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.6331 -1.9735  0.2795  1.8090  4.4940 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.213e+02  3.090e+00  39.250   <2e-16 ***
## Snaps       -2.742e-04  2.136e-03  -0.128    0.898    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.074 on 289 degrees of freedom
## Multiple R-squared:  5.699e-05,  Adjusted R-squared:  -0.003403 
## F-statistic: 0.01647 on 1 and 289 DF,  p-value: 0.898

Mid Frequency

Mid Frequency - SPL

## 
## Call:
## lm(formula = SPL_Midrange ~ Tot_Knocks, data = AC.DF1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.2088 -2.1924 -0.7869  1.6962 11.9299 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 1.045e+02  3.773e-01 277.047  < 2e-16 ***
## Tot_Knocks  1.801e-02  4.252e-03   4.237 3.54e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.302 on 189 degrees of freedom
## Multiple R-squared:  0.08674,    Adjusted R-squared:  0.08191 
## F-statistic: 17.95 on 1 and 189 DF,  p-value: 3.538e-05

Mid Frequency - ACI

## 
## Call:
## glm(formula = ACI_Midrange ~ Tot_Knocks + Year, family = "Gamma", 
##     data = AC.DF1)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.24710  -0.14537  -0.07297   0.11790   0.40777  
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.746e-05  3.758e-07  46.459   <2e-16 ***
## Tot_Knocks  -8.617e-09  3.462e-09  -2.489   0.0137 *  
## Year18       2.779e-07  4.078e-07   0.682   0.4964    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Gamma family taken to be 0.02745441)
## 
##     Null deviance: 4.9867  on 190  degrees of freedom
## Residual deviance: 4.8131  on 188  degrees of freedom
## AIC: 4038.2
## 
## Number of Fisher Scoring iterations: 4
## 
## Call:
## glm(formula = ACI_Midrange ~ Num_L_calls + Year, family = "Gamma", 
##     data = AC.DF1)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.19561  -0.15304  -0.06392   0.11642   0.42225  
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.690e-05  3.382e-07  49.964   <2e-16 ***
## Num_L_calls -4.017e-09  2.953e-08  -0.136    0.892    
## Year18       2.304e-07  4.140e-07   0.557    0.579    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Gamma family taken to be 0.02823657)
## 
##     Null deviance: 4.9867  on 190  degrees of freedom
## Residual deviance: 4.9772  on 188  degrees of freedom
## AIC: 4044.6
## 
## Number of Fisher Scoring iterations: 4
## 
## Call:
## glm(formula = ACI_Midrange ~ Num_Herbivory + Year, family = "Gamma", 
##     data = AC.DF1)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.22182  -0.15000  -0.06905   0.11317   0.42714  
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    1.697e-05  3.019e-07  56.198   <2e-16 ***
## Num_Herbivory -2.940e-08  2.290e-08  -1.284    0.201    
## Year18         2.350e-07  4.112e-07   0.571    0.568    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Gamma family taken to be 0.02795665)
## 
##     Null deviance: 4.9867  on 190  degrees of freedom
## Residual deviance: 4.9338  on 188  degrees of freedom
## AIC: 4042.9
## 
## Number of Fisher Scoring iterations: 4
## 
## Call:
## glm(formula = ACI_Midrange ~ Tot_Knocks + Site + Year + Hour, 
##     family = "Gamma", data = AC.DF1)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.23464  -0.14810  -0.02786   0.09402   0.40045  
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.687e-05  5.893e-07  28.620  < 2e-16 ***
## Tot_Knocks  -6.857e-09  4.115e-09  -1.666  0.09738 .  
## Site35      -3.948e-07  6.308e-07  -0.626  0.53219    
## Site40       1.842e-06  6.744e-07   2.731  0.00694 ** 
## Site5       -1.827e-07  7.031e-07  -0.260  0.79525    
## Site8       -2.771e-07  6.134e-07  -0.452  0.65206    
## Year18       2.542e-07  3.925e-07   0.648  0.51800    
## Hour21       6.213e-07  5.771e-07   1.077  0.28311    
## Hour3        6.336e-07  5.689e-07   1.114  0.26689    
## Hour9        1.735e-07  5.654e-07   0.307  0.75935    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Gamma family taken to be 0.02532824)
## 
##     Null deviance: 4.9867  on 190  degrees of freedom
## Residual deviance: 4.3779  on 181  degrees of freedom
## AIC: 4034
## 
## Number of Fisher Scoring iterations: 4

Breakdown by Site - SPL

Breakdown by Site - ACI

Mid Frequency - Hourly Breakdown

Breakdown by Hour - SPL

Breakdown by Hour - ACI

Mid Frequency Hourly Breakdown (Long Calls)

3 AM, long calls don’t seem to explain a great deal of the relationship at any site

9 AM, long calls don’t seem to explain the relationship at any site

3 PM, long calls don’t seem to explain the relationship

9 PM, long calls don’t seem to explain the relationship

Mid Frequency Hourly Breakdown (Herbivory)

3 AM, Extremely low herbivory at all sites. No relationship

Again, extremely low herbivory, no relationship.

Higher herbivory. Seems like there is a relationship at site 40, 8, and 35.

Higher herbivory here as well, although there is no positive relationship at any site.

Summary Knocks significantly explained SPLMF at sites 35 and 32 and at 9AM.

Supplementary Diurnal Plots

Acoustics Breakdown All acoustic metrics (SPL and ACI) are broken down into 2 frequency bands: High Frequency (Frequencies between 1 kHz - 22 kHz) and Mid Frequency (Frequencies between 160 Hz and 1 kHz)

Note 2017 had a 10 minute duty cycle with 5 minutes recording while 2018 had a 15 minute duty cycle with 5 minutes recording, so the number of files averages differs between years

Diurnal Deployment Plots - Supplementary

Total Deployment Plots

Models

Preliminary Models Looking into the relationships between biogenic sounds (Knocks/Calls and Snaps) and their frequency spectra (MF SPL/HF SPL) respectively.

Testing for Distribution

shapiro.test(AC.DF1$SPL_Midrange)
## 
##  Shapiro-Wilk normality test
## 
## data:  AC.DF1$SPL_Midrange
## W = 0.92679, p-value = 3.406e-08
qqnorm(AC.DF1$SPL_Midrange)

#ks.test(SPLHF.long$SPL_HF, "pnorm", mean=mean(SPLHF.long$SPL_HF), sd=sd(SPLHF.long$SPL_HF))

#ks.test(SPLMF.long$SPL_MF, "pnorm", mean=mean(SPLMF.long$SPL_MF), sd=sd(SPLMF.long$SPL_MF))

ggplot(data = Snap.HF, aes(Snap.HF$SPL_HF)) + geom_histogram() + ggtitle("HF SPL distribution")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(data = AC.DF1, aes(AC.DF1$ACI_Midrange)) + geom_histogram() + ggtitle("MF ACI distribution")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(data = AC.DF1, aes(AC.DF1$ACI_HF)) + geom_histogram() + ggtitle("HF ACI distribution")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

gamma_test(AC.DF1$ACI_Midrange)
## 
##  Test of fit for the Gamma distribution
## 
## data:  AC.DF1$ACI_Midrange
## V = 4.3336, p-value = 0.002182
gamma_test(AC.DF1$ACI_HF)
## 
##  Test of fit for the Gamma distribution
## 
## data:  AC.DF1$ACI_HF
## V = 4.9011, p-value = 0.0005291
gamma_test(Snap.HF$SPL_HF)
## 
##  Test of fit for the Gamma distribution
## 
## data:  Snap.HF$SPL_HF
## V = 7.8948, p-value = 2.372e-08

Don’t seem to have a normal distribution here… Working on testing different distributions. Can’t find what the p-values indicate for these gamma tests

Mid-Frequency SPL Model

Maximal Model

Maximal Model with Bill

fit.m <- lm(SPL_Midrange ~(Tot_Knocks + Num_Herbivory + Num_L_calls)*(Site + Hour) + Year, data = AC.DF1Co)
summary(fit.m)
## 
## Call:
## lm(formula = SPL_Midrange ~ (Tot_Knocks + Num_Herbivory + Num_L_calls) * 
##     (Site + Hour) + Year, data = AC.DF1Co)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2170 -1.2622 -0.1569  1.1008  5.9507 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.040e+02  1.039e+00 100.154  < 2e-16 ***
## Tot_Knocks            6.742e-03  1.513e-02   0.446 0.656421    
## Num_Herbivory         2.019e-01  3.082e-01   0.655 0.513320    
## Num_L_calls          -4.731e-02  1.181e-01  -0.401 0.689255    
## Site35                9.601e-01  1.166e+00   0.823 0.411629    
## Site40               -2.755e+00  1.070e+00  -2.574 0.010960 *  
## Site5                -5.481e-01  1.095e+00  -0.501 0.617374    
## Site8                -1.808e+00  1.038e+00  -1.743 0.083340 .  
## Hour21                8.820e-01  5.437e-01   1.622 0.106767    
## Hour3                -2.264e+00  2.092e+00  -1.082 0.280983    
## Hour9                 2.618e+00  2.096e+00   1.249 0.213552    
## Year18                3.925e+00  3.196e-01  12.282  < 2e-16 ***
## Tot_Knocks:Site35    -1.458e-02  1.432e-02  -1.018 0.310289    
## Tot_Knocks:Site40     1.099e-02  1.726e-02   0.636 0.525394    
## Tot_Knocks:Site5     -1.831e-02  1.408e-02  -1.301 0.195163    
## Tot_Knocks:Site8     -1.516e-02  1.522e-02  -0.996 0.320693    
## Tot_Knocks:Hour21     8.699e-03  1.092e-02   0.797 0.426879    
## Tot_Knocks:Hour3      1.184e-02  1.102e-02   1.074 0.284454    
## Tot_Knocks:Hour9      4.361e-02  1.171e-02   3.723 0.000273 ***
## Num_Herbivory:Site35 -1.447e-01  3.092e-01  -0.468 0.640479    
## Num_Herbivory:Site40 -5.393e-01  3.150e-01  -1.712 0.088813 .  
## Num_Herbivory:Site5  -2.400e-01  3.076e-01  -0.780 0.436461    
## Num_Herbivory:Site8  -7.112e-02  3.085e-01  -0.231 0.817956    
## Num_Herbivory:Hour21 -6.096e-04  8.470e-02  -0.007 0.994267    
## Num_Herbivory:Hour3  -7.106e-01  6.836e-01  -1.040 0.300117    
## Num_Herbivory:Hour9   5.260e-01  7.094e-01   0.741 0.459511    
## Num_L_calls:Site35    2.410e-01  1.910e-01   1.262 0.208822    
## Num_L_calls:Site40    1.828e-01  1.078e-01   1.696 0.091819 .  
## Num_L_calls:Site5    -7.132e-02  1.396e-01  -0.511 0.610178    
## Num_L_calls:Site8     4.688e-02  1.028e-01   0.456 0.648863    
## Num_L_calls:Hour21    8.163e-02  9.719e-02   0.840 0.402248    
## Num_L_calls:Hour3     3.101e-02  1.165e-01   0.266 0.790544    
## Num_L_calls:Hour9    -2.675e-01  1.351e-01  -1.980 0.049427 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.041 on 158 degrees of freedom
## Multiple R-squared:  0.7084, Adjusted R-squared:  0.6493 
## F-statistic:    12 on 32 and 158 DF,  p-value: < 2.2e-16
stepAIC(fit.m)
## Start:  AIC=302.21
## SPL_Midrange ~ (Tot_Knocks + Num_Herbivory + Num_L_calls) * (Site + 
##     Hour) + Year
## 
##                      Df Sum of Sq     RSS    AIC
## - Num_Herbivory:Hour  3      6.83  664.69 298.19
## - Tot_Knocks:Site     4     24.83  682.68 301.29
## <none>                             657.86 302.21
## - Num_L_calls:Site    4     36.35  694.20 304.48
## - Num_L_calls:Hour    3     41.50  699.35 307.90
## - Num_Herbivory:Site  4     79.04  736.90 315.88
## - Tot_Knocks:Hour     3     92.30  750.16 321.29
## - Year                1    628.11 1285.96 428.24
## 
## Step:  AIC=298.19
## SPL_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Hour + Year + Tot_Knocks:Site + Tot_Knocks:Hour + Num_Herbivory:Site + 
##     Num_L_calls:Site + Num_L_calls:Hour
## 
##                      Df Sum of Sq     RSS    AIC
## - Tot_Knocks:Site     4     24.85  689.54 297.20
## <none>                             664.69 298.19
## - Num_L_calls:Site    4     35.64  700.33 300.16
## - Num_L_calls:Hour    3     40.27  704.96 303.42
## - Tot_Knocks:Hour     3     88.49  753.18 316.06
## - Num_Herbivory:Site  4     96.88  761.56 316.17
## - Year                1    647.13 1311.81 426.04
## 
## Step:  AIC=297.2
## SPL_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Hour + Year + Tot_Knocks:Hour + Num_Herbivory:Site + Num_L_calls:Site + 
##     Num_L_calls:Hour
## 
##                      Df Sum of Sq     RSS    AIC
## <none>                             689.54 297.20
## - Num_L_calls:Site    4     36.89  726.43 299.15
## - Num_L_calls:Hour    3     50.99  740.52 304.82
## - Num_Herbivory:Site  4    101.98  791.52 315.54
## - Tot_Knocks:Hour     3    101.17  790.70 317.34
## - Year                1    655.66 1345.20 422.84
## 
## Call:
## lm(formula = SPL_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + 
##     Site + Hour + Year + Tot_Knocks:Hour + Num_Herbivory:Site + 
##     Num_L_calls:Site + Num_L_calls:Hour, data = AC.DF1Co)
## 
## Coefficients:
##          (Intercept)            Tot_Knocks         Num_Herbivory  
##           103.883544             -0.004243              0.281592  
##          Num_L_calls                Site35                Site40  
##            -0.026390              1.211723             -3.008499  
##                Site5                 Site8                Hour21  
##            -0.733301             -1.642642              0.779976  
##                Hour3                 Hour9                Year18  
##            -0.199326              1.006530              3.904610  
##    Tot_Knocks:Hour21      Tot_Knocks:Hour3      Tot_Knocks:Hour9  
##             0.009165              0.009517              0.040037  
## Num_Herbivory:Site35  Num_Herbivory:Site40   Num_Herbivory:Site5  
##            -0.223915             -0.607692             -0.328665  
##  Num_Herbivory:Site8    Num_L_calls:Site35    Num_L_calls:Site40  
##            -0.148352              0.223663              0.137930  
##    Num_L_calls:Site5     Num_L_calls:Site8    Num_L_calls:Hour21  
##            -0.132447              0.004349              0.109991  
##    Num_L_calls:Hour3     Num_L_calls:Hour9  
##             0.050565             -0.257516

Best MF-SPL Model

Next is the best model from AIC stepwise model selection

#SPL_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + Hour + Year + Tot_Knocks:Site + Tot_Knocks:Hour + Num_Herbivory:Site + Num_L_calls:Site + Num_L_calls:Hour

fit.m2 <- lm(SPL_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + Hour + Year + Tot_Knocks:Site + Tot_Knocks:Hour + Num_Herbivory:Site + Num_L_calls:Site + Num_L_calls:Hour, data = AC.DF1Co)

Anova(fit.m2, type=3)
## Anova Table (Type III tests)
## 
## Response: SPL_Midrange
##                    Sum Sq  Df    F value    Pr(>F)    
## (Intercept)         44532   1 10786.5010 < 2.2e-16 ***
## Tot_Knocks              1   1     0.1624 0.6874574    
## Num_Herbivory           4   1     0.9933 0.3204412    
## Num_L_calls             1   1     0.1826 0.6697040    
## Site                  120   4     7.2699 2.087e-05 ***
## Hour                   42   3     3.3839 0.0196605 *  
## Year                  647   1   156.7463 < 2.2e-16 ***
## Tot_Knocks:Site        25   4     1.5048 0.2032243    
## Tot_Knocks:Hour        88   3     7.1449 0.0001554 ***
## Num_Herbivory:Site     97   4     5.8663 0.0001968 ***
## Num_L_calls:Site       36   4     2.1582 0.0760730 .  
## Num_L_calls:Hour       40   3     3.2514 0.0233376 *  
## Residuals             665 161                         
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(fit.m2)
## 
## Call:
## lm(formula = SPL_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + 
##     Site + Hour + Year + Tot_Knocks:Site + Tot_Knocks:Hour + 
##     Num_Herbivory:Site + Num_L_calls:Site + Num_L_calls:Hour, 
##     data = AC.DF1Co)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.2174 -1.2322 -0.1251  1.0980  5.9555 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          104.206794   1.003358 103.858  < 2e-16 ***
## Tot_Knocks             0.005885   0.014603   0.403 0.687457    
## Num_Herbivory          0.278351   0.279293   0.997 0.320441    
## Num_L_calls           -0.050139   0.117328  -0.427 0.669704    
## Site35                 0.766076   1.120805   0.684 0.495270    
## Site40                -2.936460   1.041347  -2.820 0.005408 ** 
## Site5                 -0.742531   1.046012  -0.710 0.478813    
## Site8                 -2.085095   0.990076  -2.106 0.036756 *  
## Hour21                 0.879295   0.538575   1.633 0.104501    
## Hour3                 -0.168172   0.562300  -0.299 0.765265    
## Hour9                  1.120116   0.608855   1.840 0.067653 .  
## Year18                 3.942663   0.314913  12.520  < 2e-16 ***
## Tot_Knocks:Site35     -0.013232   0.014091  -0.939 0.349122    
## Tot_Knocks:Site40      0.011545   0.017084   0.676 0.500151    
## Tot_Knocks:Site5      -0.017482   0.013708  -1.275 0.204032    
## Tot_Knocks:Site8      -0.015266   0.014960  -1.020 0.309036    
## Tot_Knocks:Hour21      0.008873   0.010204   0.869 0.385874    
## Tot_Knocks:Hour3       0.012101   0.010872   1.113 0.267341    
## Tot_Knocks:Hour9       0.042694   0.011519   3.706 0.000289 ***
## Num_Herbivory:Site35  -0.221091   0.281598  -0.785 0.433530    
## Num_Herbivory:Site40  -0.611817   0.298717  -2.048 0.042169 *  
## Num_Herbivory:Site5   -0.317416   0.282805  -1.122 0.263369    
## Num_Herbivory:Site8   -0.147308   0.280869  -0.524 0.600671    
## Num_L_calls:Site35     0.247525   0.189782   1.304 0.194006    
## Num_L_calls:Site40     0.183437   0.106859   1.717 0.087970 .  
## Num_L_calls:Site5     -0.069899   0.138445  -0.505 0.614327    
## Num_L_calls:Site8      0.053260   0.101700   0.524 0.601206    
## Num_L_calls:Hour21     0.080441   0.096709   0.832 0.406763    
## Num_L_calls:Hour3      0.044625   0.115290   0.387 0.699218    
## Num_L_calls:Hour9     -0.258808   0.133308  -1.941 0.053953 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.032 on 161 degrees of freedom
## Multiple R-squared:  0.7054, Adjusted R-squared:  0.6523 
## F-statistic: 13.29 on 29 and 161 DF,  p-value: < 2.2e-16
plot(fit.m2)

Interaction Plots

## NULL
## NULL

Mid-Frequency ACI Model

Maximal Model

Maximal model following Bill’s method

  • gamma distribution due to the left skew of the data
fit.a <- glm(ACI_Midrange ~(Tot_Knocks + Num_Herbivory + Num_L_calls)*(Site + Hour) + Year, data = AC.DF1Co, family = "Gamma")
summary(fit.a)
## 
## Call:
## glm(formula = ACI_Midrange ~ (Tot_Knocks + Num_Herbivory + Num_L_calls) * 
##     (Site + Hour) + Year, family = "Gamma", data = AC.DF1Co)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.24879  -0.12333  -0.02497   0.08025   0.36994  
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.690e-05  1.444e-06  11.699   <2e-16 ***
## Tot_Knocks           -2.546e-08  1.928e-08  -1.321    0.188    
## Num_Herbivory         3.467e-07  4.468e-07   0.776    0.439    
## Num_L_calls          -3.403e-08  1.565e-07  -0.217    0.828    
## Site35               -1.184e-06  1.608e-06  -0.736    0.463    
## Site40                1.624e-06  1.531e-06   1.061    0.290    
## Site5                -1.438e-06  1.512e-06  -0.952    0.343    
## Site8                -5.345e-07  1.453e-06  -0.368    0.713    
## Hour21                6.913e-07  7.114e-07   0.972    0.333    
## Hour3                -1.930e-06  2.549e-06  -0.757    0.450    
## Hour9                 3.315e-06  3.230e-06   1.026    0.306    
## Year18                3.223e-07  4.236e-07   0.761    0.448    
## Tot_Knocks:Site35     1.090e-08  1.827e-08   0.597    0.551    
## Tot_Knocks:Site40     2.652e-08  2.402e-08   1.104    0.271    
## Tot_Knocks:Site5      2.536e-08  1.802e-08   1.407    0.161    
## Tot_Knocks:Site8      2.288e-08  1.972e-08   1.160    0.248    
## Tot_Knocks:Hour21     6.822e-09  1.391e-08   0.490    0.625    
## Tot_Knocks:Hour3     -8.492e-10  1.403e-08  -0.061    0.952    
## Tot_Knocks:Hour9      6.244e-09  1.483e-08   0.421    0.674    
## Num_Herbivory:Site35 -2.623e-07  4.484e-07  -0.585    0.559    
## Num_Herbivory:Site40 -3.463e-07  4.595e-07  -0.754    0.452    
## Num_Herbivory:Site5  -3.652e-07  4.459e-07  -0.819    0.414    
## Num_Herbivory:Site8  -3.946e-07  4.468e-07  -0.883    0.379    
## Num_Herbivory:Hour21 -1.418e-07  1.063e-07  -1.335    0.184    
## Num_Herbivory:Hour3  -8.192e-07  8.323e-07  -0.984    0.326    
## Num_Herbivory:Hour9   1.189e-06  1.088e-06   1.093    0.276    
## Num_L_calls:Site35    1.946e-08  2.478e-07   0.079    0.938    
## Num_L_calls:Site40    6.352e-08  1.454e-07   0.437    0.663    
## Num_L_calls:Site5    -4.761e-08  1.803e-07  -0.264    0.792    
## Num_L_calls:Site8     1.097e-09  1.343e-07   0.008    0.993    
## Num_L_calls:Hour21    3.364e-09  1.307e-07   0.026    0.979    
## Num_L_calls:Hour3    -1.778e-07  1.564e-07  -1.137    0.257    
## Num_L_calls:Hour9    -1.595e-07  1.741e-07  -0.916    0.361    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Gamma family taken to be 0.02551326)
## 
##     Null deviance: 4.9867  on 190  degrees of freedom
## Residual deviance: 3.8459  on 158  degrees of freedom
## AIC: 4055.2
## 
## Number of Fisher Scoring iterations: 4
stepAIC(fit.a)
## Start:  AIC=4055.17
## ACI_Midrange ~ (Tot_Knocks + Num_Herbivory + Num_L_calls) * (Site + 
##     Hour) + Year
## 
##                      Df Deviance    AIC
## - Num_L_calls:Site    4   3.8643 4047.9
## - Tot_Knocks:Hour     3   3.8658 4049.9
## - Tot_Knocks:Site     4   3.9294 4050.4
## - Num_L_calls:Hour    3   3.9306 4052.5
## - Num_Herbivory:Site  4   3.9975 4053.1
## - Num_Herbivory:Hour  3   3.9531 4053.4
## - Year                1   3.8606 4053.7
## <none>                    3.8459 4055.2
## 
## Step:  AIC=4048.08
## ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Hour + Year + Tot_Knocks:Site + Tot_Knocks:Hour + Num_Herbivory:Site + 
##     Num_Herbivory:Hour + Num_L_calls:Hour
## 
##                      Df Deviance    AIC
## - Tot_Knocks:Hour     3   3.8849 4042.9
## - Tot_Knocks:Site     4   3.9547 4043.7
## - Num_Herbivory:Hour  3   3.9652 4046.1
## - Num_L_calls:Hour    3   3.9659 4046.1
## - Num_Herbivory:Site  4   4.0246 4046.5
## - Year                1   3.8747 4046.5
## <none>                    3.8643 4048.1
## 
## Step:  AIC=4043.1
## ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Hour + Year + Tot_Knocks:Site + Num_Herbivory:Site + Num_Herbivory:Hour + 
##     Num_L_calls:Hour
## 
##                      Df Deviance    AIC
## - Tot_Knocks:Site     4   3.9597 4038.1
## - Num_Herbivory:Hour  3   3.9721 4040.6
## - Num_L_calls:Hour    3   3.9864 4041.2
## - Num_Herbivory:Site  4   4.0413 4041.4
## - Year                1   3.8959 4041.5
## <none>                    3.8849 4043.1
## 
## Step:  AIC=4038.76
## ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Hour + Year + Num_Herbivory:Site + Num_Herbivory:Hour + Num_L_calls:Hour
## 
##                      Df Deviance    AIC
## - Num_Herbivory:Hour  3   4.0359 4035.9
## - Num_L_calls:Hour    3   4.0467 4036.3
## - Year                1   3.9627 4036.9
## - Num_Herbivory:Site  4   4.1360 4037.9
## - Tot_Knocks          1   3.9995 4038.4
## <none>                    3.9597 4038.8
## 
## Step:  AIC=4036.41
## ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Hour + Year + Num_Herbivory:Site + Num_L_calls:Hour
## 
##                      Df Deviance    AIC
## - Num_L_calls:Hour    3   4.1075 4033.3
## - Year                1   4.0389 4034.5
## - Num_Herbivory:Site  4   4.2302 4036.3
## <none>                    4.0359 4036.4
## - Tot_Knocks          1   4.0871 4036.5
## 
## Step:  AIC=4033.78
## ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Hour + Year + Num_Herbivory:Site
## 
##                      Df Deviance    AIC
## - Hour                3   4.1672 4030.2
## - Year                1   4.1094 4031.9
## - Num_Herbivory:Site  4   4.3010 4033.6
## <none>                    4.1075 4033.8
## - Tot_Knocks          1   4.1576 4033.8
## - Num_L_calls         1   4.1776 4034.6
## 
## Step:  AIC=4030.55
## ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Year + Num_Herbivory:Site
## 
##                      Df Deviance    AIC
## - Year                1   4.1686 4028.6
## - Tot_Knocks          1   4.2086 4030.2
## - Num_L_calls         1   4.2113 4030.3
## <none>                    4.1672 4030.5
## - Num_Herbivory:Site  4   4.3652 4030.6
## 
## Step:  AIC=4028.61
## ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + 
##     Num_Herbivory:Site
## 
##                      Df Deviance    AIC
## - Tot_Knocks          1   4.2092 4028.3
## - Num_L_calls         1   4.2137 4028.4
## <none>                    4.1686 4028.6
## - Num_Herbivory:Site  4   4.3721 4028.9
## 
## Step:  AIC=4028.47
## ACI_Midrange ~ Num_Herbivory + Num_L_calls + Site + Num_Herbivory:Site
## 
##                      Df Deviance    AIC
## - Num_L_calls         1   4.2572 4028.4
## <none>                    4.2092 4028.5
## - Num_Herbivory:Site  4   4.4228 4029.2
## 
## Step:  AIC=4028.64
## ACI_Midrange ~ Num_Herbivory + Site + Num_Herbivory:Site
## 
## Call:  glm(formula = ACI_Midrange ~ Num_Herbivory + Site + Num_Herbivory:Site, 
##     family = "Gamma", data = AC.DF1Co)
## 
## Coefficients:
##          (Intercept)         Num_Herbivory                Site35  
##            1.795e-05             3.282e-07            -1.544e-06  
##               Site40                 Site5                 Site8  
##            9.005e-07            -1.530e-06            -1.156e-06  
## Num_Herbivory:Site35  Num_Herbivory:Site40   Num_Herbivory:Site5  
##           -2.453e-07            -3.617e-07            -3.830e-07  
##  Num_Herbivory:Site8  
##           -3.881e-07  
## 
## Degrees of Freedom: 190 Total (i.e. Null);  181 Residual
## Null Deviance:       4.987 
## Residual Deviance: 4.257     AIC: 4029
AICc(fit.a, ACI.mf.lm)
##           df     AICc
## fit.a     34 4070.423
## ACI.mf.lm  4 4038.392

Best Model

Most parsimonious and best model from the AIC stepwise model selection

#ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + Hour + Year + Num_Herbivory:Site
fit.a2 <- glm(ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + Site + Hour + Num_Herbivory:Site, data = AC.DF1Co, family = "Gamma")
summary(fit.a2)
## 
## Call:
## glm(formula = ACI_Midrange ~ Tot_Knocks + Num_Herbivory + Num_L_calls + 
##     Site + Hour + Num_Herbivory:Site, family = "Gamma", data = AC.DF1Co)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.24565  -0.13928  -0.02445   0.09444   0.38612  
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           1.765e-05  1.247e-06  14.159   <2e-16 ***
## Tot_Knocks           -5.791e-09  4.065e-09  -1.424   0.1561    
## Num_Herbivory         3.515e-07  4.013e-07   0.876   0.3823    
## Num_L_calls          -5.311e-08  3.028e-08  -1.754   0.0811 .  
## Site35               -1.617e-06  1.255e-06  -1.288   0.1993    
## Site40                1.023e-06  1.277e-06   0.801   0.4244    
## Site5                -1.279e-06  1.285e-06  -0.995   0.3209    
## Site8                -1.117e-06  1.241e-06  -0.900   0.3692    
## Hour21                6.821e-07  6.162e-07   1.107   0.2699    
## Hour3                 4.663e-07  6.153e-07   0.758   0.4495    
## Hour9                -8.317e-08  6.137e-07  -0.136   0.8924    
## Num_Herbivory:Site35 -2.689e-07  4.043e-07  -0.665   0.5069    
## Num_Herbivory:Site40 -3.351e-07  4.185e-07  -0.801   0.4244    
## Num_Herbivory:Site5  -4.007e-07  4.039e-07  -0.992   0.3225    
## Num_Herbivory:Site8  -4.079e-07  4.026e-07  -1.013   0.3123    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for Gamma family taken to be 0.02451643)
## 
##     Null deviance: 4.9867  on 190  degrees of freedom
## Residual deviance: 4.1094  on 176  degrees of freedom
## AIC: 4031.9
## 
## Number of Fisher Scoring iterations: 4

High Frequency ACI Model

Distribution

ggplot(data =Snap.HF, aes(Snap.HF$ACI_HF)) + geom_histogram() + ggtitle("HF ACI distribution") + geom_vline(aes(xintercept = mean(ACI_HF)), color = "red", linetype ="dashed", size = 1) + geom_vline(aes(xintercept = median(ACI_HF)), color = "blue", linetype = "dotted", size = 1)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Distribution looks normal, given what we discussed about the HF SPL distribution

Maximal Model

#testing time splits for this model to confirm they are the same as SPL HF model
afit.tg <- lm(ACI_HF ~ Snaps*tg*Site + Year, data = Snap.HFC)
afit.dn <- lm(ACI_HF ~ Snaps*dn*Site + Year, data = Snap.HFC)
afit.ns <- lm(ACI_HF ~ Snaps*ns*Site + Year, data = Snap.HFC)
afit.t12 <- lm(ACI_HF ~Snaps*t12*Site + Year, data = Snap.HFC)



AICc(afit.tg, afit.dn, afit.ns, afit.t12)
##          df     AICc
## afit.tg  42 318203.3
## afit.dn  22 318276.9
## afit.ns  32 318292.4
## afit.t12 22 318159.7
fit.hfaci <- lm(ACI_HF ~ Snaps*t12 + Snaps*Site + t12*Site + Year, data = Snap.HFC)
fit.hfaci2 <- lm(ACI_HF ~ Snaps*t12*Site + Year, data = Snap.HFC)
fit.hfaci3 <- lm(ACI_HF ~ Snaps*t12 + Snaps*Site + Year, data = Snap.HFC)

AICc(fit.hfaci,fit.hfaci2, fit.hfaci3)
##            df     AICc
## fit.hfaci  18 318164.8
## fit.hfaci2 22 318159.7
## fit.hfaci3 14 318393.5
summary(fit.hfaci2)
## 
## Call:
## lm(formula = ACI_HF ~ Snaps * t12 * Site + Year, data = Snap.HFC)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12613.4  -3641.7   -958.7   2729.3  21530.1 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -2.883e+05  1.821e+05  -1.583  0.11351    
## Snaps               -5.588e+00  2.739e+00  -2.040  0.04135 *  
## t12Low              -1.203e+03  1.866e+02  -6.445 1.19e-10 ***
## Site35               4.440e+03  2.333e+02  19.033  < 2e-16 ***
## Site40               3.104e+01  2.469e+02   0.126  0.89996    
## Site5                4.635e+02  1.972e+02   2.350  0.01880 *  
## Site8                3.123e+03  1.827e+02  17.096  < 2e-16 ***
## Year                 1.739e+02  9.029e+01   1.927  0.05406 .  
## Snaps:t12Low         8.336e+00  3.251e+00   2.564  0.01034 *  
## Snaps:Site35         9.194e-01  4.078e+00   0.225  0.82164    
## Snaps:Site40        -7.411e+00  4.369e+00  -1.696  0.08987 .  
## Snaps:Site5          1.576e+00  4.318e+00   0.365  0.71516    
## Snaps:Site8         -1.934e+01  3.950e+00  -4.896 9.85e-07 ***
## t12Low:Site35        5.579e+02  3.166e+02   1.762  0.07806 .  
## t12Low:Site40        2.276e+02  3.241e+02   0.702  0.48259    
## t12Low:Site5         3.701e+03  2.738e+02  13.519  < 2e-16 ***
## t12Low:Site8        -4.602e+02  3.445e+02  -1.336  0.18169    
## Snaps:t12Low:Site35 -6.317e+00  5.227e+00  -1.209  0.22683    
## Snaps:t12Low:Site40 -9.996e+00  5.456e+00  -1.832  0.06693 .  
## Snaps:t12Low:Site5  -1.329e+01  5.584e+00  -2.380  0.01733 *  
## Snaps:t12Low:Site8  -1.707e+01  5.080e+00  -3.360  0.00078 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5069 on 15966 degrees of freedom
## Multiple R-squared:  0.1587, Adjusted R-squared:  0.1577 
## F-statistic: 150.6 on 20 and 15966 DF,  p-value: < 2.2e-16
stepAIC(fit.hfaci2)
## Start:  AIC=272788.5
## ACI_HF ~ Snaps * t12 * Site + Year
## 
##                  Df Sum of Sq        RSS    AIC
## <none>                        4.1026e+11 272788
## - Year            1  95367893 4.1035e+11 272790
## - Snaps:t12:Site  4 338278009 4.1059e+11 272794
## 
## Call:
## lm(formula = ACI_HF ~ Snaps * t12 * Site + Year, data = Snap.HFC)
## 
## Coefficients:
##         (Intercept)                Snaps               t12Low  
##          -2.883e+05           -5.587e+00           -1.203e+03  
##              Site35               Site40                Site5  
##           4.440e+03            3.104e+01            4.635e+02  
##               Site8                 Year         Snaps:t12Low  
##           3.123e+03            1.739e+02            8.336e+00  
##        Snaps:Site35         Snaps:Site40          Snaps:Site5  
##           9.194e-01           -7.411e+00            1.576e+00  
##         Snaps:Site8        t12Low:Site35        t12Low:Site40  
##          -1.934e+01            5.579e+02            2.276e+02  
##        t12Low:Site5         t12Low:Site8  Snaps:t12Low:Site35  
##           3.701e+03           -4.602e+02           -6.317e+00  
## Snaps:t12Low:Site40   Snaps:t12Low:Site5   Snaps:t12Low:Site8  
##          -9.996e+00           -1.329e+01           -1.707e+01
IP4 <- interaction.plot(Snap.HFC$t12, Snap.HFC$Site, Snap.HF$ACI_HF)

So it looks like ACI has a significant 3 way interaction at site 5… WHAT DOES THIS MEAN AND HOW DO I SHOW IT

Show it - I think I can make a 2 frame plot, facet_wrap by time, showing the effect between Snaps and ACI in each plot

What does it mean - it means that HF ACI is significantly associated with combined changes of Snaps and Time and Site (but only at site 5?)

#fit.hfaci <- lm(ACI_HF ~(Snaps*t12*Site) + Year, data = Snap.HF)
#summary(fit.hfaci)
#stepAIC(fit.a)

#AICc(fit.a, ACI.mf.lm)

High Frequency SPL Model

Manual Model Selection

Determining which is the best way to group the snaps by time

tg = quarters (00-05, 06-11, 12-17, 18-23) dn = day night (18-05, 6-17) ns = nine cycle (22-03, 04-09, 10-15, 16-21) t12 = my half and half cycle (2140 - 920, 920 - 2140)

fit.tg <- lm(SPL_HF ~ Snaps*tg*Site + Year, data = Snap.HFC)
fit.dn <- lm(SPL_HF ~ Snaps*dn*Site + Year, data = Snap.HFC)
fit.ns <- lm(SPL_HF ~ Snaps*ns*Site + Year, data = Snap.HFC)
fit.t12 <- lm(SPL_HF ~Snaps*t12*Site + Year, data = Snap.HFC)

#models that have a 2 way interaction and time seperately as a factor
fit.t12t <- lm(SPL_HF ~ Snaps*Site + t12 + Year, data = Snap.HFC)
fit.tgt <- lm(SPL_HF ~ Snaps*Site + tg + Year, data = Snap.HFC)
fit.dnt <- lm(SPL_HF ~ Snaps*Site + dn + Year, data = Snap.HFC)
fit.nst <- lm(SPL_HF ~ Snaps*Site + ns + Year, data = Snap.HFC)

AICc(fit.tg, fit.dn, fit.ns, fit.t12, fit.t12t, fit.tgt, fit.dnt, fit.nst)
##          df     AICc
## fit.tg   42 68564.26
## fit.dn   22 72450.05
## fit.ns   32 70408.03
## fit.t12  22 64311.29
## fit.t12t 13 65331.35
## fit.tgt  15 70314.51
## fit.dnt  13 72650.42
## fit.nst  14 71856.06

Best Model

Best model was the one that split time at 9:20 and 21:40

Confused about my next steps here

stepAIC(fit.t12)
## Start:  AIC=18940.08
## SPL_HF ~ Snaps * t12 * Site + Year
## 
##                  Df Sum of Sq   RSS   AIC
## <none>                        52137 18940
## - Snaps:t12:Site  4      1087 53223 19262
## - Year            1     35884 88021 27311
## 
## Call:
## lm(formula = SPL_HF ~ Snaps * t12 * Site + Year, data = Snap.HFC)
## 
## Coefficients:
##         (Intercept)                Snaps               t12Low  
##          -6.687e+03           -8.989e-03           -2.886e+00  
##              Site35               Site40                Site5  
##          -1.421e+00           -1.297e+00           -1.782e+00  
##               Site8                 Year         Snaps:t12Low  
##           1.615e+00            3.374e+00            5.547e-03  
##        Snaps:Site35         Snaps:Site40          Snaps:Site5  
##           3.703e-02            1.997e-02            8.580e-03  
##         Snaps:Site8        t12Low:Site35        t12Low:Site40  
##           5.426e-03           -7.920e-02           -8.341e-01  
##        t12Low:Site5         t12Low:Site8  Snaps:t12Low:Site35  
##          -1.815e+00           -2.476e+00           -3.223e-02  
## Snaps:t12Low:Site40   Snaps:t12Low:Site5   Snaps:t12Low:Site8  
##          -7.714e-03           -2.101e-03           -9.700e-03
#returned only the three way interaction - so I am going to try some manual selection to see if there is a more parsimonious model

fit.hf1 <- lm(SPL_HF ~ Snaps + t12 + Site + Snaps:t12 + Snaps:Site + t12:Site, data = Snap.HFC)
fit.hf2 <- lm(SPL_HF ~ Snaps + t12 + Site + Snaps:t12 + Snaps:Site, data = Snap.HFC)
fit.hf3 <- lm(SPL_HF ~ Snaps + Site + Snaps:Site, data = Snap.HFC)

AICc(fit.t12,fit.hf1, fit.hf2, fit.hf3)
##         df     AICc
## fit.t12 22 64311.29
## fit.hf1 17 73122.38
## fit.hf2 13 73615.19
## fit.hf3 11 78480.77
#SPL_HF ~ Snaps + t12 + Site + Snaps:t12 + Snaps:Site + t12:Site

snap.model <- lm(SPL_HF ~ Snaps + t12 + Site + Snaps:t12 + Snaps:Site + t12:Site, data = Snap.HFC)

Anova(fit.t12, type = 3)
## Anova Table (Type III tests)
## 
## Response: SPL_HF
##                Sum Sq    Df   F value    Pr(>F)    
## (Intercept)     34636     1 10606.698 < 2.2e-16 ***
## Snaps             277     1    84.770 < 2.2e-16 ***
## t12              6147     1  1882.447 < 2.2e-16 ***
## Site             9383     4   718.363 < 2.2e-16 ***
## Year            35884     1 10989.000 < 2.2e-16 ***
## Snaps:t12          75     1    22.915 1.709e-06 ***
## Snaps:Site       2628     4   201.172 < 2.2e-16 ***
## t12:Site         2166     4   165.863 < 2.2e-16 ***
## Snaps:t12:Site   1087     4    83.194 < 2.2e-16 ***
## Residuals       52137 15966                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(fit.t12)
## 
## Call:
## lm(formula = SPL_HF ~ Snaps * t12 * Site + Year, data = Snap.HFC)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.0059 -1.1523 -0.0511  1.0325  9.5333 
## 
## Coefficients:
##                       Estimate Std. Error  t value Pr(>|t|)    
## (Intercept)         -6.687e+03  6.493e+01 -102.989  < 2e-16 ***
## Snaps               -8.989e-03  9.763e-04   -9.207  < 2e-16 ***
## t12Low              -2.886e+00  6.652e-02  -43.387  < 2e-16 ***
## Site35              -1.421e+00  8.317e-02  -17.087  < 2e-16 ***
## Site40              -1.297e+00  8.802e-02  -14.738  < 2e-16 ***
## Site5               -1.782e+00  7.031e-02  -25.344  < 2e-16 ***
## Site8                1.615e+00  6.512e-02   24.808  < 2e-16 ***
## Year                 3.374e+00  3.219e-02  104.828  < 2e-16 ***
## Snaps:t12Low         5.547e-03  1.159e-03    4.787 1.71e-06 ***
## Snaps:Site35         3.703e-02  1.454e-03   25.471  < 2e-16 ***
## Snaps:Site40         1.997e-02  1.558e-03   12.819  < 2e-16 ***
## Snaps:Site5          8.580e-03  1.539e-03    5.574 2.52e-08 ***
## Snaps:Site8          5.426e-03  1.408e-03    3.853 0.000117 ***
## t12Low:Site35       -7.920e-02  1.129e-01   -0.702 0.482821    
## t12Low:Site40       -8.341e-01  1.155e-01   -7.219 5.49e-13 ***
## t12Low:Site5        -1.815e+00  9.759e-02  -18.596  < 2e-16 ***
## t12Low:Site8        -2.476e+00  1.228e-01  -20.156  < 2e-16 ***
## Snaps:t12Low:Site35 -3.223e-02  1.863e-03  -17.297  < 2e-16 ***
## Snaps:t12Low:Site40 -7.714e-03  1.945e-03   -3.967 7.32e-05 ***
## Snaps:t12Low:Site5  -2.101e-03  1.991e-03   -1.056 0.291199    
## Snaps:t12Low:Site8  -9.700e-03  1.811e-03   -5.357 8.59e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.807 on 15966 degrees of freedom
## Multiple R-squared:  0.7323, Adjusted R-squared:  0.7319 
## F-statistic:  2183 on 20 and 15966 DF,  p-value: < 2.2e-16
plot(fit.t12)

hist(resid(snap.model))

Interaction Plots

## NULL
## NULL
## NULL

Plots_for_Publishing

Plots for use in paper

High Frequency Plots

This first plot uses ALL data (2017 & 2018) and all sites

It seems super crowded, so maybe we only need to display a piece of it?

Here is a plot using only one site (Site 5)

Mid Frequency Plots

This plot uses ALL data (2017 & 2018) and all sites/hours

Way too much going on.

Here is a plot that only uses 9am

This shows that the pattern exists at pretty much all sites except for 5. I think this is the plot to go with.

Combination Plot

HF ACI Plots

Diurnal Plot

##   [1] "21:00" "21:10" "21:20" "21:30" "21:40" "21:50" "22:00" "22:10"
##   [9] "22:20" "22:30" "22:40" "22:50" "23:00" "23:10" "23:20" "23:30"
##  [17] "23:40" "23:50" "0:00"  "0:10"  "0:20"  "0:30"  "0:40"  "0:50" 
##  [25] "1:00"  "1:10"  "1:20"  "1:30"  "1:40"  "1:50"  "2:00"  "2:10" 
##  [33] "2:20"  "2:30"  "2:40"  "2:50"  "3:00"  "3:10"  "3:20"  "3:30" 
##  [41] "3:40"  "3:50"  "4:00"  "4:10"  "4:20"  "4:30"  "4:40"  "4:50" 
##  [49] "5:00"  "5:10"  "5:20"  "5:30"  "5:40"  "5:50"  "6:00"  "6:10" 
##  [57] "6:20"  "6:30"  "6:40"  "6:50"  "7:00"  "7:10"  "7:20"  "7:30" 
##  [65] "7:40"  "7:50"  "8:00"  "8:10"  "8:20"  "8:30"  "8:40"  "8:50" 
##  [73] "9:00"  "9:10"  "9:20"  "9:30"  "9:40"  "9:50"  "10:00" "10:10"
##  [81] "10:20" "10:30" "10:40" "10:50" "11:00" "11:10" "11:20" "11:30"
##  [89] "11:40" "11:50" "12:00" "12:10" "12:20" "12:30" "12:40" "12:50"
##  [97] "13:00" "13:10" "13:20" "13:30" "13:40" "13:50" "14:00" "14:10"
## [105] "14:20" "14:30" "14:40" "14:50" "15:00" "15:10" "15:20" "15:30"
## [113] "15:40" "15:50" "16:00" "16:10" "16:20" "16:30" "16:40" "16:50"
## [121] "17:00" "17:10" "17:20" "17:30" "17:40" "17:50" "18:00" "18:10"
## [129] "18:20" "18:30" "18:40" "18:50" "19:00" "19:10" "19:20" "19:30"
## [137] "19:40" "19:50" "20:00" "20:10" "20:20" "20:30" "20:40" "20:50"
## [145] "11:45" "12:15" "12:45" "13:15" "13:45" "14:15" "14:45" "15:15"
## [153] "15:45" "16:15" "16:45" "17:15" "17:45" "18:15" "18:45" "19:15"
## [161] "19:45" "20:15" "20:45" "21:15" "21:45" "22:15" "22:45" "23:15"
## [169] "23:45" "0:15"  "0:45"  "1:15"  "1:45"  "2:15"  "2:45"  "3:15" 
## [177] "3:45"  "4:15"  "4:45"  "5:15"  "5:45"  "6:15"  "6:45"  "7:15" 
## [185] "7:45"  "8:15"  "8:45"  "9:15"  "9:45"  "10:15" "10:45" "11:15"

Point Plot

##   [1] "21:00" "21:10" "21:20" "21:30" "21:40" "21:50" "22:00" "22:10"
##   [9] "22:20" "22:30" "22:40" "22:50" "23:00" "23:10" "23:20" "23:30"
##  [17] "23:40" "23:50" "0:00"  "0:10"  "0:20"  "0:30"  "0:40"  "0:50" 
##  [25] "1:00"  "1:10"  "1:20"  "1:30"  "1:40"  "1:50"  "2:00"  "2:10" 
##  [33] "2:20"  "2:30"  "2:40"  "2:50"  "3:00"  "3:10"  "3:20"  "3:30" 
##  [41] "3:40"  "3:50"  "4:00"  "4:10"  "4:20"  "4:30"  "4:40"  "4:50" 
##  [49] "5:00"  "5:10"  "5:20"  "5:30"  "5:40"  "5:50"  "6:00"  "6:10" 
##  [57] "6:20"  "6:30"  "6:40"  "6:50"  "7:00"  "7:10"  "7:20"  "7:30" 
##  [65] "7:40"  "7:50"  "8:00"  "8:10"  "8:20"  "8:30"  "8:40"  "8:50" 
##  [73] "9:00"  "9:10"  "9:20"  "9:30"  "9:40"  "9:50"  "10:00" "10:10"
##  [81] "10:20" "10:30" "10:40" "10:50" "11:00" "11:10" "11:20" "11:30"
##  [89] "11:40" "11:50" "12:00" "12:10" "12:20" "12:30" "12:40" "12:50"
##  [97] "13:00" "13:10" "13:20" "13:30" "13:40" "13:50" "14:00" "14:10"
## [105] "14:20" "14:30" "14:40" "14:50" "15:00" "15:10" "15:20" "15:30"
## [113] "15:40" "15:50" "16:00" "16:10" "16:20" "16:30" "16:40" "16:50"
## [121] "17:00" "17:10" "17:20" "17:30" "17:40" "17:50" "18:00" "18:10"
## [129] "18:20" "18:30" "18:40" "18:50" "19:00" "19:10" "19:20" "19:30"
## [137] "19:40" "19:50" "20:00" "20:10" "20:20" "20:30" "20:40" "20:50"
## [145] "11:45" "12:15" "12:45" "13:15" "13:45" "14:15" "14:45" "15:15"
## [153] "15:45" "16:15" "16:45" "17:15" "17:45" "18:15" "18:45" "19:15"
## [161] "19:45" "20:15" "20:45" "21:15" "21:45" "22:15" "22:45" "23:15"
## [169] "23:45" "0:15"  "0:45"  "1:15"  "1:45"  "2:15"  "2:45"  "3:15" 
## [177] "3:45"  "4:15"  "4:45"  "5:15"  "5:45"  "6:15"  "6:45"  "7:15" 
## [185] "7:45"  "8:15"  "8:45"  "9:15"  "9:45"  "10:15" "10:45" "11:15"

HF SPL Plots

Diurnal Plot

Point Plot

##   [1] "21:00" "21:10" "21:20" "21:30" "21:40" "21:50" "22:00" "22:10"
##   [9] "22:20" "22:30" "22:40" "22:50" "23:00" "23:10" "23:20" "23:30"
##  [17] "23:40" "23:50" "0:00"  "0:10"  "0:20"  "0:30"  "0:40"  "0:50" 
##  [25] "1:00"  "1:10"  "1:20"  "1:30"  "1:40"  "1:50"  "2:00"  "2:10" 
##  [33] "2:20"  "2:30"  "2:40"  "2:50"  "3:00"  "3:10"  "3:20"  "3:30" 
##  [41] "3:40"  "3:50"  "4:00"  "4:10"  "4:20"  "4:30"  "4:40"  "4:50" 
##  [49] "5:00"  "5:10"  "5:20"  "5:30"  "5:40"  "5:50"  "6:00"  "6:10" 
##  [57] "6:20"  "6:30"  "6:40"  "6:50"  "7:00"  "7:10"  "7:20"  "7:30" 
##  [65] "7:40"  "7:50"  "8:00"  "8:10"  "8:20"  "8:30"  "8:40"  "8:50" 
##  [73] "9:00"  "9:10"  "9:20"  "9:30"  "9:40"  "9:50"  "10:00" "10:10"
##  [81] "10:20" "10:30" "10:40" "10:50" "11:00" "11:10" "11:20" "11:30"
##  [89] "11:40" "11:50" "12:00" "12:10" "12:20" "12:30" "12:40" "12:50"
##  [97] "13:00" "13:10" "13:20" "13:30" "13:40" "13:50" "14:00" "14:10"
## [105] "14:20" "14:30" "14:40" "14:50" "15:00" "15:10" "15:20" "15:30"
## [113] "15:40" "15:50" "16:00" "16:10" "16:20" "16:30" "16:40" "16:50"
## [121] "17:00" "17:10" "17:20" "17:30" "17:40" "17:50" "18:00" "18:10"
## [129] "18:20" "18:30" "18:40" "18:50" "19:00" "19:10" "19:20" "19:30"
## [137] "19:40" "19:50" "20:00" "20:10" "20:20" "20:30" "20:40" "20:50"
## [145] "11:45" "12:15" "12:45" "13:15" "13:45" "14:15" "14:45" "15:15"
## [153] "15:45" "16:15" "16:45" "17:15" "17:45" "18:15" "18:45" "19:15"
## [161] "19:45" "20:15" "20:45" "21:15" "21:45" "22:15" "22:45" "23:15"
## [169] "23:45" "0:15"  "0:45"  "1:15"  "1:45"  "2:15"  "2:45"  "3:15" 
## [177] "3:45"  "4:15"  "4:45"  "5:15"  "5:45"  "6:15"  "6:45"  "7:15" 
## [185] "7:45"  "8:15"  "8:45"  "9:15"  "9:45"  "10:15" "10:45" "11:15"